Splitting of normal modes and travel time anomalies due to the magnetic field of the Earth

Abstract

We examine the effects of a toroidal magnetic field on two types of seismic data: first, on splitting of normal modes and, second, on body wave travel times. The main contribution of this paper is the derivation of formulas for these problems. Comparison between data and theory indicates that the magnitude of the toroidal magnetic field (T20) has to be as large as 250 T (tesla) to explain the data. There are, however, some inconsistencies among the fit to the data set. For example, some modes require a strong magnetic field near the core mantle boundary, while other modes require a weak field. Also the travel time difference between polar and equatorial paths is not explained by the T10 or T20 field. A field with odd angular degree 𝓁 (T𝓁0 or S𝓁0) is needed to produce the travel time difference between the polar and equatorial paths. We also point out that ohmic dissipation due to a strong magnetic field with 100 T is about 4–5 orders of magnitude larger than the present heat flow output of the Earth. The analysis suggests that the magnetic field in the outer core is not the cause of seismic anomalies.